Direction: What should come in place of question mark in the following number series?
1 3 9 39 249 2559 ?

Options

A. 28561
B. 30458
C. 32589
D. 352289

Answer

To solve the number series: 1, 3, 9, 39, 249, 2559, ?, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The series starts with 1 and seems to be increasing rapidly. We will look for a pattern involving multiplication and addition.

2. **Calculate the Differences**:
- From 1 to 3: \(1 + 2 = 3\)
- From 3 to 9: \(3 \times 3 = 9\)
- From 9 to 39: \(9 \times 4 + 3 = 39\)
- From 39 to 249: \(39 \times 6 + 15 = 249\)
- From 249 to 2559: \(249 \times 10 + 9 = 2559\)

3. **Establish the Multiplication and Addition Pattern**:
- The pattern seems to involve multiplying by increasing integers and then adding a certain number.
- The multipliers appear to be 2, 3, 4, 6, 10, and we need to find the next multiplier.

4. **Finding the Next Multiplier**:
- The multipliers are not in a simple arithmetic progression, but they seem to be increasing in a non-linear fashion.
- Let's assume the next multiplier after 10 is 12 (as we are skipping some numbers).

5. **Calculate the Next Number**:
- Using the last number in the series (2559):
- If we multiply by 12 and add a number (which we will assume to be 15, following the previous pattern):
\[ 2559 \times 12 + 15 \]
- First, calculate \(2559 \times 12\):
\[ 2559 \times 12 = 30708 \]
- Now add 15:
\[ 30708 + 15 = 30723 \]

6. **Final Answer**:
- The next number in the series is **30723**.